We propose MiNNIE, a simple yet comprehensive framework for real-time simulation of nonlinear near-incompressible elastics. To avoid the common volumetric locking issues at high Poisson's ratios of linear finite element methods (FEM), we build MiNNIE upon a mixed FEM framework and further incorporate a pressure stabilization term to ensure excellent convergence of multigrid solvers. Our pressure stabilization strategy injects bounded influence on nodal displacement which can be eliminated using a quasi-Newton method. MiNNIE has a specially tailored GPU multigrid solver including a modified skinning-space interpolation scheme, a novel vertex Vanka smoother, and an efficient dense solver using Schur complement. MiNNIE supports various elastic material models and simulates them in real-time, supporting a full range of Poisson's ratios up to 0.5 while handling large deformations, element inversions, and self-collisions at the same time.